NCERT Solutions for Class 10 Maths Chapter 12

NCERT Solutions for class 10 Maths Chapter 12 Exercise 12.3, Exercise 12.2 & Exercise 12.1 (प्रश्नावली 12.1, प्रश्नावली 12.2 & प्रश्नावली 12.3) of Areas related to Circles in Hindi and English Medium PDF form for UP Board & CBSE Education to free download. Download NCERT Textbooks for class 10 all subjects in PDF form. Solutions are prepared according to Latest CBSE Syllabus for the academic year 2018-19. Previous years questions related to this chapter are given below and links for their answers are also given with the questions.

Previous Years Questions

Three marks questions

In the given figure, OACB is a quadrant of a circle with centre O and radius 3.5 cm. If OD = 2 cm, find the area of the shaded region. [CBSE 2017]

Four marks questions

In the given figure, the side of square is 28 cm and radius of each circle is half of the length of the side of the square where O and O’ are the centres of the circles. Find the area of the shaded region. [CBSE 2017]

2. A chord PQ of a circle of radius 10 cm subtends an angle of 60 at the centre of circle. Find the area of major and minor segments of the circle. [CBSE 2017]

Objective of the Area Related to Circles

To find the circumference, area of a circle and circular paths. To derive and understand the formulae for perimeter and area of a sector of a circle. To find the perimeter and the area of a sector, using the above formulae. Finding the areas of some combinations of figures involving circles, sectors as well as triangles, squares, rectangles and solve daily life problems based on perimeters and areas of various plane figures.

Formulae for perimeters and areas of various figures:

Perimeter of a rectangle = 2 (length + breadth)

Area of a rectangle = length × breadth

Perimeter of a square = 4 × side

Area of a square = (side) × (side)

Area of a parallelogram = base × corresponding altitude

Area of a triangle = 1/2 × base × corresponding altitude

Area of a rhombus = 1/2 × product of its diagonals

Area of a trapezium = 1/2 × (sum of the two parallel sides) × distance between them

Circumference of a circle = 2 × π × radius

Area of a circle = π × (radius) × (radius)

Area of a sector = angle/360 × π × (radius) × (radius)

Length of an arc = angle/360 × 2π × (radius)

Perimeter of a sector = angle/360 × 2π × (radius) + 2(radius)

Area of segment = Area of sector – area of triangle

Historical Facts!

All the mathematical ideas have emerged out of daily life experiences. The first ever need of human being was counting objects. This gave rise to the idea of numbers. When the man learn to grow crops, following types of problems had to be handled:

Fencing or constructing some kind of a boundary around the field, where the crops were to be grown.

Allotting lands of different sizes for growing different crops.

Making suitable places for storing different products grown under different crops.

These problems led to the need of measurement of perimeters (lengths), areas and volumes, which in turn gave rise to a branch of mathematics known as Mensuration. Area related to circle is one of the part of mensuration.